Virtually all sequence-based spread spectrum systems are based on the interpretation of a stream of independent and identically distributed (iid) random variables translated to discrete phase words. These phase words are subsequently combined as a time series into a bandlimited spread spectrum communications signal, and traditionally combined via spreading operations with phase-shift keying (PSK)-based data words. In direct sequence spread spectrum (DSSS) modulations, the discrete phase words are typically selected as 2-ary or 4-ary PSK-based spread modulations, effectively representing a higher rate version of a standard BPSK or QPSK modulation. In chaotic sequence spread spectrum (CSSS) modulations, the discrete phase words may be represented as arbitrary-phase modulations that are drawn as nearly random points on the unit circle, representable by phases such as 28-ary up to 216-ary PSK modulations. The increased order of the representative PSK modulation produces a whiter overall spectral response. Ignoring windowing effects, the spectral content can be approximated as consisting of concentrations of energy represented by the phase difference between each successive iid phase word (instantaneous frequency being approximated as the rate of change of phase within the chosen chip periods), which if drawn from a uniform distribution, will also be uniform, and therefore generate an approximately white communications signal.